Why crowds get dumber when they watch each other — and the surprisingly expensive curePrečo davy hlúpnu, keď sa pozerajú jeden na druhého — a prekvapivo drahá náprava

The "wisdom of crowds" is real: average enough independent guesses and the errors cancel, so a large group beats almost any individual. But that magic rests on a fragile word — independent. We ran three simulations to find exactly how it breaks, and the cure turned out to be far more expensive than the usual advice admits.

1. A crowd that watches actions collapses to the wisdom of ~3 people

Put rational agents in a line. Each gets a private clue and sees what everyone before them did (not why). Each updates like a perfect Bayesian. The result: once a few early choices line up, the next person's own clue is outweighed by the public tally, so they rationally ignore it and follow the crowd — and everyone after inherits the same frozen belief.

Measured: a crowd of 1,001 such agents has the effective wisdom of about 3 independent minds (accuracy flat from N=3 to N=1,001, while 1,001 independent voters approach certainty). The √N improvement that makes crowds powerful is simply gone. No one was irrational; the information structure was.

2. It takes only two visible neighbours to trigger it

You might think herding needs a densely connected network. It does not. We varied how many predecessors each agent can see. With zero they're independent and the crowd is near-perfect; watching one neighbour still mostly works; watching two already collapses accuracy to the individual level — and it stays collapsed no matter how many more they watch. The threshold is sharp and shockingly low, and it has a clean formula: a cascade begins the moment observed decisions outweigh your trust in your own evidence.

3. The cheap cure doesn't work — you need most of the room independent

The standard fix is to add a devil's advocate or a contrarian quota. We tested it: force a fraction of agents to ignore the crowd and vote their own clue. It barely helps. At a 10–30% contrarian quota the crowd is no better than the pure herd; even making half the group independent yields almost nothing. Collective accuracy only recovers past roughly 80% forced independence. The reason: the herd is a correlated bloc that piles onto the early consensus and swamps the scattered independent voices.

What to actually do

Diversity injected into a herding process is dominated, not amplified. So the fix is structural, not a token role:

• Collect views before exposure. Sealed forecasts, blind estimates, write-then-reveal — most people

must form a position before seeing others'.

• Share evidence, not verdicts. A channel that carries reasons keeps the independent information

alive; a channel that carries conclusions invites copying.

• Distrust unanimity. A committee, market, or AI agent-swarm that quickly agrees may be revealing its

wiring, not the truth.

What would change our mind

These are simulations of sequential decision-observation. If members can transmit their full evidence (not just a choice), the cascade never forms and the collapse disappears — that is the design lesson, not a loophole. And if the independent voices act first — seeding a correct public prior before any herding begins — the required fraction should drop sharply. Order-of-arrival is the obvious next test, and a low threshold there would refine "how much independence" into "independence when."

The headline stands on measured numbers, each with a stated falsifier: a herd of a thousand is worth three; two visible neighbours are enough to cause it; and rescuing it costs most of the room.